xvii, 1238 pages : 24 cm

Includes bibliographical references and index

Mathematics in Mesopotamia -- Egyptian mathematics -- The creation of classical Greek mathematics -- Euclid and Apollonius -- The Alexandrian Greek period : geometry and trigonometry -- The Alexandrian period : the reemergence of arithmetic and algebra -- The Greek rationalization of nature -- The demise of the Greek world -- The mathematics of the Hindus and Arabs -- The Medieval Period in Europe -- The Renaissance -- Mathematical contributions in the Renaissance -- Arithmetic and algebra in the sixteenth and seventeenth centuries -- The beginning of projective geometry -- Coordinate geometry -- The mathematization of science -- The creation of the calculus -- Mathematics as of 1700 -- Calculus in the eighteenth century -- Infinite series -- Ordinary differential equations in the eighteenth century -- Partial differential equations in the eighteenth century -- Analytic and differential geometry in the eighteenth century -- The calculus of variations in the eighteenth century -- Algebra in the eighteenth century -- Mathematics as of 1800 -- Functions of a complex variable -- Partial differential equations in the nineteenth century -- Ordinary differential equations in the nineteenth century -- The calculus of variations in the nineteenth century -- Galois theory-- Quaternions, vectors, and linear associative algebras -- Determinants and matrices -- The theory of numbers in the nineteenth century -- The revival of projective geometry -- Non-Euclidean geometry -- The differential geometry of Gauss and Riemann -- Projective and metric geometry -- Algebraic geometry -- The instillation of rigor in analysis -- The foundations of the real and transfinite numbers -- The foundations of geometry -- Mathematics as of 1900 -- The theory of functions of real variables -- Integral equations -- Functional analysis -- Divergent series -- Tensor analysis and differential geometry -- The emergence of abstract algebra -- The beginnings of topology -- The foundations of mathematics

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